Building Functions Test – Algebra 1 Math (Printable PDF)

Question 1 Plumber Rates (2 points)

A plumber charges $65 per visit plus $48 per hour.

1. Write a function C(h) for the cost of a visit lasting h hours. (1 point)
2. Find the cost of a 2.5-hour visit. (1 point)

Question 2 Recursive to Explicit (2 points)

A balance follows A(0) = 500 and A(n) = A(n − 1) − 35. Write an explicit rule and find A(8).

Question 3 Linear Table (2 points)

A table gives y = 11, 20, 32 for x = 2, 5, 9. Show that y changes at a constant rate and write the rule.

Question 4 Combine Two Functions (3 points)

Let f(x) = 2x² − x and g(x) = 5x + 3.

1. Find (f + g)(x). (1 point)
2. Find (f − g)(x). (1 point)
3. Find (f · g)(−1). (1 point)

Question 5 Break-Even for a Bake Sale (3 points)

A bake sale has revenue R(x) = 22x and cost C(x) = 300 + 10x dollars for x boxes. The graph shows both.

1. Write the profit function. (1 point)
2. Find the break-even number of boxes. (1 point)
3. Find the profit for 40 boxes. (1 point)

Question 6 Inverse of a Linear Function (3 points)

Let f(x) = 5x − 8.

1. Find f⁻¹(x). (2 points)
2. Check your answer by computing f⁻¹(f(3)). (1 point)

Question 7 Rental Hours (3 points)

A bike rental costs R(h) = 8h + 15 dollars for h hours.

1. Find a function that gives the hours for a total cost R. (2 points)
2. How many hours can a customer rent for $63? (1 point)

Question 8 Candle Height (2 points)

A candle is 14 inches tall and burns down 0.75 inch per hour, so its height is h(t) = 14 − 0.75t.

1. Explain why this is a linear function and interpret the slope. (1 point)
2. Find the height after 6 hours. (1 point)